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Simplifying 3x(2x + 4) + 9(2x + 4) = 0 Reorder the terms: 3x(4 + 2x) + 9(2x + 4) = 0 (4 * 3x + 2x * 3x) + 9(2x + 4) = 0 (12x + 6x2) + 9(2x + 4) = 0 Reorder the terms: 12x + 6x2 + 9(4 + 2x) = 0 12x + 6x2 + (4 * 9 + 2x * 9) = 0 12x + 6x2 + (36 + 18x) = 0 Reorder the terms: 36 + 12x + 18x + 6x2 = 0 Combine like terms: 12x + 18x = 30x 36 + 30x + 6x2 = 0 Solving 36 + 30x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(6 + 5x + x2) = 0 Factor a trinomial. 6((3 + x)(2 + x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-3, -2}
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